Multi-domain spectral approach for the Hilbert transform on the real line

01/07/2021

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by   C. Klein, et al.

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A multi-domain spectral method is presented to compute the Hilbert transform on the whole compactified real line, with a special focus on piece-wise analytic functions and functions with algebraic decay towards infinity. Several examples of these and other types of functions are discussed. As an application solitons to generalized Benjamin-Ono equations are constructed.